Gore perhaps after airgun exploded, covering uniform first (9)
I believe the answer is:
inaugural
'first' is the definition.
(I know this)
'gore perhaps after airgun exploded covering uniform' is the wordplay.
'gore perhaps' becomes 'al' (Al Gore, former vice president of the US).
'after' is a charade indicator (letters next to each other).
'exploded' indicates an anagram.
'covering' means one lot of letters goes inside another.
'uniform' becomes 'U' (phonetic alphabet: alpha, bravo, charlie etc.).
'airgun' is an anagram of 'inaugr'.
'inaugr' enclosing 'u' is 'inaugur'.
'al' put after 'inaugur' is 'INAUGURAL'.
(Other definitions for inaugural that I've seen before include "First address" , "Maiden" , "Of an opening ceremony" , "Of a ceremony officially marking the beginning of something" , "President's address" .)